Robust Improvement in Estimation of a Covariance Matrix in an Elliptically Contoured Distribution Respect to Quadratic Loss Function
Let S be matrix of residual sum of square in linear model Y = Aβ + e where matrix e is distributed as elliptically contoured with unknown scale matrix Σ. In present work, we consider the problem of estimating Σ with respect to squared loss function, L(Σˆ , Σ) = tr(ΣΣˆ −1 −I) 2 . It is shown th...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Islamic Azad University
2008-03-01
|
| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/36 |
| Summary: | Let S be matrix of residual sum of square in linear
model Y = Aβ + e where matrix e is distributed as elliptically
contoured with unknown scale matrix Σ. In present work, we consider
the problem of estimating Σ with respect to squared loss
function, L(Σˆ , Σ) = tr(ΣΣˆ −1 −I)
2
. It is shown that improvement
of the estimators were obtained by James, Stein [7], Dey and Srivasan
[1] under the normality assumption remains robust under an
elliptically contoured distribution respect to squared loss function |
|---|---|
| ISSN: | 1735-8299 1735-8299 |